Mean from a frequency table calculator

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Enter each value (or class, like 10-20) with its frequency, and the calculator finds the mean. For grouped data it uses the midpoint of each class and gives an estimate:

\bar{x} = \frac{\sum fx}{\sum f}

$\sum fx$ is the total of each value multiplied by its frequency, and $\sum f$ is the total frequency (how many values there are altogether).

Value or class (e.g. 10-20)Frequency

Mean

1.45

Σfx = 29, Σf = 20

Working

1Multiply each value by its frequency: 0 × 4 = 0; 1 × 6 = 6; 2 × 7 = 14; 3 × 3 = 9
2Total of f × x = 29; total frequency = 20
3Mean = 29 ÷ 20 = 1.45

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Worked example: ungrouped data

The number of goals scored in 20 matches:

Goals (x)	Frequency (f)	fx
0	4	0
1	6	6
2	7	14
3	3	9
Total	20	29

Mean $= 29 \div 20 = 1.45$ goals.

Worked example: grouped data

Time (minutes)	Frequency	Midpoint	f × midpoint
0-10	5	5	25
10-20	8	15	120
20-30	7	25	175
Total	20		320

Estimated mean $= 320 \div 20 = 16$ minutes. It's an estimate because we don't know the exact values in each class: the midpoint stands in for all of them.

Median and mode from a table

Mode: the value with the highest frequency (2 goals above); for grouped data, the modal class.
Median: the middle value. With 20 values it's halfway between the 10th and 11th. Count down the frequencies: values 1 to 4 are 0, 5 to 10 are 1, 11 to 17 are 2. So the 10th is 1 and the 11th is 2, and the median is 1.5.

Why divide by Σf

A common mistake is dividing by the number of rows (4 here) instead of the total frequency (20). The mean is the total of all the values divided by how many values there are, and each row stands for several values.

Common mistakes

Dividing by the number of rows.
Adding the frequencies instead of the fx column on top.
Using the class boundaries instead of the midpoint for grouped data.

Practise with our mean from a frequency table questions and see the mean, median and mode calculator for a plain list.

Exam tips

Add an fx column to the table in the exam: it earns method marks.
Say "estimate" for grouped data.
Check your mean lies within the range of the data.

Frequently asked questions

How do you find the mean from a frequency table?

Multiply each value by its frequency, add those products, then divide by the total frequency: Σfx ÷ Σf.

How do you estimate the mean from grouped data?

Use the midpoint of each class as its value, multiply by the frequency, add up, and divide by the total frequency.

Why is the mean from grouped data only an estimate?

The exact values in each class aren't known, so the midpoint is used in place of every value in that class.

Is anything I type sent to a server?

No. The calculation runs in your browser and nothing is stored.

Sources

GCSE mathematics: subject content and assessment objectives. Department for Education.
Cambridge IGCSE Mathematics 0580 syllabus. Cambridge International.

Mean from a frequency table questions and answers

8 GCSE and IGCSE questions with worked answers, checked as you type.

Mean, median, mode and range calculator

Mean, median, mode and range for any list of numbers, with the working explained.

Mean, median, mode and range questions and answers